非凸优化问题的组合同伦方法

The Combined Homotopy Methods for Nonconvex Optimization Problem

借鉴已有的理论结果,研究具体一类非凸约束区域上优化问题的组合同伦方法的实现。针对这类非凸约束区域,给出了拟法锥的构造方法,证明了所选映射关于约束梯度是正独立的、可行域关于所选映射是满足拟法锥条件的,构造了拟法锥条件下的组合同伦方程,给出了数值例子。

Drawing lessons from the ready theories results, this paper deals with the achievement of optimization problem about combined holnotopy interior point method （CHIP） on concrete a type of noneonvex constrained domain. Contraposing to this nonconvex constrained domain, we give the structure methcd of the quasi - normal. Prove the chosen mappings on constrained grads are positive independent, the chosen mapping on constraints feasible set satisfy the quasi - normal cone condition, and construct combined homotopy equation under the quasi - normal cone condi- tion with numerical value and examples.